Trigonometry
Transform the given rectangular equation into a polar equation.
5x + 2y = 9
x = 12
x2 + y2 = 361
(x - 5)2 + y2 =25
Transform the given polar equation into a rectangular equation. Use the resulting equation to draw the graph.
r = 4
r = 2 csc θ
r = 8 cos θ
r = 8 cos θ + 10 sin θ
Transform the given polar equation into a rectangular equation. Find the slope and the y-intercept of the resulting equation.
r sin (θ − π/3) = 4
Convert the given coordinates into rectangular coordinates. Find the distance between the resulting points.
(4, 3π/4) and (8, π/4)
Which of the following polar coordinates represents the same location as (4, 80°)?
I. (4, 440°)
II. (-4, 260°)
III. (-4, 300°)
IV. (-4, -100°)
Which of the following polar coordinates represents the same location as (8, 210°)?
I. (8, 390°)
II. (-8, 50°)
III. (8, 410°)
IV. (-8, 30°)
Which of the following polar coordinates represents the same location as (5, -5π/4)?
I. (5, 3π/4)
II. (5, π/6)
III. (-5, -9π/4)
IV. (-5, -2π)
Which of the following polar coordinates represents the same location as (-6, 2π/3)?
I. (-6, 4π/3)
II. (-6, 11π/3)
III. (6, 11π/3)
IV. (6, -π/3)
Which of the following polar coordinates represents the same location as (-10, -π/6)?
I. (10, 17π/6)
II. (-10, 15π/6)
III. (10, 13π/6)
IV. (-10, 11π/6)
Which of the following polar coordinates represents the same location as (-15, 5π)?
I. (-15, 8π)
II. (-15, -π)
III. (15, 8π)
IV. (15, 4π)
Convert the following polar coordinates to rectangular coordinates:
(15, 270°)
(-12, 3π/2)
(13.4, 5.3)
Convert the following rectangular coordinates to polar coordinates. Write the angle in radians:
(-8, 8)
(21, -7√3)
Consider the following equation.
r = 10 + 7 cos θ
Perform the test for symmetry with respect to the polar axis, the line θ = π/2, and the pole.
(-10, -10√3)
(0, 13)
The following point has polar coordinates. Plot it in a polar coordinate system. Then, determine another point that has the same location as the given in which r > 0 and 4π < θ < 6π:
(7, π/3)
The following point has polar coordinates. Plot it in a polar coordinate system. Then, determine another point that has the same location as the given in which r < 0 and 0 < θ < 2π:
(9, 3π/2)
Plot the provided complex number using the formula eiθ = cos θ + i sin θ.
e(π/12)i
-e5πi
Identify the point on the graph corresponding to the provided polar coordinates, with points P, Q, R, and S indicated.
(2, 135°)
(-4, 5π/4)
(4, π)
(2, -45°)
(-4, -3π/4)
Represent the solutions in polar and rectangular form after solving the given equation in the complex number system.
x6 -64 = 0
x4 +625i = 0
x3 -(1 +i) = 0
Plot the given polar coordinates on a polar coordinate system.
(5, 60°)
(9, 90°)
(20, 5π/4)
(-15, π)
(-6, -2π/3)
Test the polar equation for symmetry and sketch its graph:
r = 12 +12 sin θ
r = 13 + cos θ
For the given equation (x +11)2 +y2 = 121, convert it to a polar equation.
Sketch the given polar equation in the polar coordinate system.
r = 5 +cos θ
r = 3/(3 - cos θ)
r = 7 + 5 sin 2θ
Convert the given polar equation to a rectangular equation and plot the polar equation using the knowledge of rectangular equation.
θ = 5π/6
r = 8 csc θ
r = 9 + 5 cos θ
r = 6 - 6 sin θ
r = 8 + 8 cos θ
r = 9 + (9/2)cos θ
r = 5 + 11 cos θ
r = 4 - 7 sin θ
r = (7/2) sin 3θ
r = 5 - 11 sin θ
r cos θ = - 7
r = 4 cos (θ/2)